New FRC Journal Paper is an Editor’s Pick at Physics of Plasmas

PFRC inventor Dr. Sam Cohen and his student Taosif Ahsan have published a new journal paper, “An analytical approach to evaluating magnetic-field closure and topological changes in FRC devices,” in Physics of Plasmas (Phys. Plasmas 29, 072507 (2022)). The paper is an Editor’s Pick and has important implications for confining plasma in Field-Reversed Configurations (FRCs).

We describe mathematical methods based on optimizing a modified non-linear flux function (MFF) to evaluate whether odd-parity perturbations affect the local closure of magnetic field lines in field-reversed configurations. Using the MFF methodology, quantitative formulas are derived that provide the shift of the field minimum and the threshold for field-line opening, a discontinuous change in field topology.

Paper Abstract

This paper follows up on a 2000 paper by Cohen and Milroy, which made qualitative assertions about changes in magnetic field topology, e.g., movement of the center of separatrix, separator line, and other geometric parameters. Ahsan and Cohen developed the modified flux function (MFF) mathematical tool to quantitatively understand the effects of perturbations on a Solov’ev FRC field structure.  The analytical results from this function have reproduced the previous numerical observation that small odd-parity perturbation preserves FRC field structure. In particular, the contours around the equilibrium stay closed.

Closure of magnetic field lines limits plasma losses that would occur due to charged particles leaving the FRC by traveling along open field lines. The paper points out that in a reactor-scale FRC where ions have a large gyroradius relative to the field structure, but electrons have a small radius and follow the field lines, particle and energy losses on the open field lines outside the FRC will be significant. Hence, ensuring closure of field lines is a crucial step toward improved plasma confinement in FRCs.

3D contours of a perturbed FRC using the modified flux function (MFF)

Princeton Fusion Systems Awarded Three DOE INFUSE 2022a Grants

The Department of Energy announced the First Round of the FY 2022 Public-Private Partnership Awards to Advance Fusion Energy. The awards list contains 18 awardees. Princeton Fusion Systems, also known as Princeton Satellite Systems, received three awards:

Electron density profiles on PFRC with USPR: Ultrashort Pulse Reflectometry (USPR) is a plasma diagnostic technique that would be used on the Princeton Field-Reversed Configuration (PFRC) to measure electron density profiles. Such profile measurements provide insight into the structure of PFRC plasma and can improve our estimates of confinement time. Our University partner is University of California, Davis, PI Dr. Neville Luhmann.

Evaluating RF antenna designs for PFRC plasma heating and sustainment: We intend to analyze RF antenna performance parameters critical to the validity of robust PFRC-type fusion reactor designs. Team member University of Rochester will support TriForce simulations and contractor Plasma Theory and Computation, Inc. will support RMF code simulations. Our national lab partner is Princeton Plasma Physics Laboratory, PI Dr. Sam Cohen.

Stabilizing PFRC plasmas against macroscopic low frequency instabilities: This award will use the TriForce code to simulate several plasma stabilization techniques for the PFRC-2 experiment. Our lab partner is PPPL and the team again includes the University of Rochester.

These awards will help us advance PFRC technology. Contact us for more information!

TriForce model of the PFRC-1 experiment

A Cutting Edge Modular Nuclear Fusion Power Plant Using PFRC Reactors

The following movie is by Woodruff Scientific, Inc. It was developed under an ARPA-E Grant. The movie shows a five PFRC modular power plant. The technician is shown for scale. Modular power plants are ideal for power systems because they allow for incremental capital investment. Modules would be added as needed. You can read more about PFRC here.

Experimental work on PFRC-2 was funded by an ARPA-E OPEN 2018 grant. ARPA-E is funding many cutting edge fusion projects including new mirror machines, stellarators and many others.

5 PFRC Modular Power Plant

ARPA-E Innovation Summit in Denver, CO

ARPA-E Summit held at Denver, CO.

It was exciting to meet and network with fusion industry and power electronics researchers, and influential leaders from both the private and public sectors at the Summit.

We displayed a prototype Class E amplifier, silicon carbide (SiC) JFET wafers, a PCB board of a load switch, and brochures of NREL.

Princeton Fusion Systems in collaboration with Princeton University, Qorvo, and NREL is developing integrated, power-dense, reliable, and scalable switching power amplifier boards for plasma heating and control applications. We presented the Class E prototype, some samples of the wide bandgap semiconductor silicon carbide (SiC) JFET wafers, and a PCB board for a load switch at our booth at the ARPA-E Summit. A previous post on our website has links to our marketing and technical documents.

The photos below show Stephanie Thomas and Sangeeta Vinoth at the Registration desk of the ARPA-E-2022-Summit.

The picture of the Class E prototype that the PFS presented at the booth has been added to the ARPA-E Innovation Summit website.

Class E prototype build by Princeton University

More pictures of the ARPA-E Summit can be found here.

The Summit helped us to understand the Fusion industry’s needs for power electronics. We design, test, and qualify circuit boards as building blocks for various applications: short pulses, control pulses, and RF amplifiers.

A key takeaway was that there was interest in SiC and GaN wide bandgap semiconductor requirements for high power and high frequency. Researchers asked about radiation-hardened electronics, and some were also interested in high voltage electronics.

There were talks at the Summit about climate change, rethinking solutions for resilience, reliability, and security of electric grid infrastructure, and decarbonization.

New Fusion Reactor Design Function

The Fusion Energy Toolbox for MATLAB is a toolbox for designing fusion reactors and for studying plasma physics. It includes a wide variety of physics and engineering tools. The latest addition to this toolbox is a new function for designing tokamaks, based on the paper in reference [1]. Tokamaks have been the leading magnetic confinement devices investigated in the pursuit of fusion net energy gain. Well-known tokamaks that either have ongoing experiments or are under development include JET, ITER, DIII-D, KSTAR, EAST, and Commonwealth Fusion Systems’ SPARC. The new capability of our toolboxes to conduct trade studies on tokamaks allows our customers to take part in this exciting field of fusion reactor design and development.

The Fusion Reactor Design function checks that the reactor satisfies key operational constraints for tokamaks. These operational constraints result from the plasma physics of the fusion reactor, where there are requirements for the plasma to remain stable (e.g., not crash into the walls) and to maintain enough electric current to help sustain itself. The tunable parameters include: the plasma minor radius ‘a’ (see figure below), the H-mode enhancement factor ‘H’, the maximum magnetic field at the coils ‘B_max’, the electric power output of the reactor ‘P_E’, and the neutron wall loading ‘P_W’, which are all essential variables to tokamak design and operation. H-mode is the high confinement mode used in many machines.

Illustration of the toroidal plasma of a tokamak. R is the major radius while a is the minor radius of the plasma. The red line represents a magnetic field line which helically winds along the torus. Image from [2].

This function captures all figure and table results in the original paper. We implemented a numerical solver which allows the user to choose a variable over which to perform a parameter sweep. A ‘mode’ option has been incorporated which allows one to select a desired parameter sweep variable (‘a’, ‘H’, ‘B_max’, ‘P_E’, or ‘P_W’) when calling the function. Some example outputs of the function are described below.

As an example, we will consider the case of tuning the maximum magnetic field at the coils ‘B_max’. The figure below plots the normalized operation constraint parameters for a tokamak as functions of B_max from 10 Tesla to 25 Tesla. The unshaded region, where the vertical axis is below the value of 1, is the region where operational constraints are met. We see that for magnetic fields below about 17.5 Tesla there is at least one operation constraint that is not met, while for higher magnetic fields all operation constraints are satisfied, thus meeting the conditions for successful operation. This high magnetic field approach is the design approach of Commonwealth Fusion Systems for the reactor they are developing [3].

Operational constraint curves as a function of B_max. Successful operation occurs if all of the curves are in the unshaded region. Note, f_B/f_NC, a ratio of the achievable to required bootstrap current, is set equal to 1. In this case P_E = 1000 MW, P_W = 4 MW/m2, and H = 1. For more details on the plotted parameters and how they function as operational plasma constraints, see reference [1].

Note, however, that there is a material cost associated with achieving higher magnetic fields, as described in reference [1]. This is illustrated in the figure below, which plots the cost parameter (the ratio of engineering components volume V_I to electric power output P_E) against B_max. There is a considerable increase in cost at high magnetic fields due to the need to add material volume that can structurally handle the higher current loads required.

Cost parameter (units of volume in cubic meters per megawatt of power, m3/MW) as a function of B_max.

In this post we illustrated the case of a tunable maximum magnetic field at the coils, though as mentioned earlier, there are other parameters you can tune. This function is part of release 2022.1 of the Fusion Energy Toolbox. Contact us at or call us at +01 609 276-9606 for more information.

Thank you to interns Emma Suh and Paige Cromley for their contributions to the development of this function.

[1] Freidberg, Mangiarotti, and Minervini, “Designing a tokamak fusion reactor–How does plasma physics fit in?”, Physics of Plasmas 22, 070901 (2015);

Posters Presented at 2021 APS Division of Plasma Physics

Our team presented a number of posters at the 63rd Annual Meeting of the APS Division of Plasma Physics, representing work supported by our ARPA-E OPEN contract and other supporting programs.

Magnetic Fusion Energy Session

Inferring electron temperature in warm hydrogen plasmas from Balmer series spectral line ratios using a collisional radiative model, Sangeeta Vinoth,

Undergraduate research

Inferring electron temperature using the collision radiative model, plasma radius = 5 cm

Modeling Spatially Resolved Neutral Atom Densities in the PFRC-2 Using DEGAS 2, Catherine Biava:

Electrostatic Energy Analyzer and Gas Stripping Cell to Measure Ion Temperature in the PFRC-2, Matthew Notis:

Consideration of Vacuum Vessel Properties Required for PFRC-type Fusion Reactors, Miles Kim,

The pulse-pile-up tail artifact in pulse-height spectra, Taosif Ahsan,

Collaborator Research

Overview of TriForce: Projects, Progress, and Plans, Adam Sefkow,

Integration of a portable spectroscopy system on the PFRC-2 device, Drew Elliott,

Kinetic simulations of the PFRC-2 using the VPIC code, Mehmet Demir,


As a follow-up to the TriAgency workshop on Compact Fusion which took place on April 28, PFS was invited to join several Fusion Industry Association members on an AIAA ASCENDx summit on June 15, “Accelerating Pathways to Space”:

Our panel on “New Opportunities in Fusion for Space Power and Propulsion” was moderated by Julie Reiss of Aerospace Corp and included us, Helicity Space, NearStar Fusion, and Tokamak Energy. You can register to rewatch our panel discussion anytime!

A key takeaway from the TriAgency workshop was that investment in compact fusion is strategic for both space and defense applications. NASA’s Ron Litchford was quoted as saying:

Compact fusion stands as a well deserving candidate for an aggressive whole-of-government R&D initiative.

Ron Litchford, Principal Technologist of NASA’s Game Changing Development Program, April 2021

We appreciated the opportunity to participate in the panel and will continue to advocate for more investment in compact fusion!